How to Calculate Distance Traveled by a Car in 4 Seconds

What is the formula to calculate the distance traveled by a car when brought to rest uniformly in 4 seconds from an initial speed of 16 meters per second?

To calculate the distance traveled by a car when brought to rest uniformly in 4 seconds from an initial speed of 16 meters per second, we can use the formula for displacement: d = ut + (1/2)at² Where: - d is the displacement or distance traveled - u is the initial velocity - a is the acceleration - t is the time traveled First, let's find the acceleration using the formula (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time taken to reach the final velocity from the initial velocity. Given: - initial velocity, u = 16 m/s - final velocity, v = 0 m/s - time, t = 4 seconds Calculating acceleration: a = (v - u) / t a = (0 - 16) / 4 a = -16 / 4 a = -4 m/s² Plugging in the values of initial velocity (u = 16) and acceleration (a = -4) into the displacement formula: d = ut + (1/2)at² d = 16t - 2t d = 16 x 4 - 2 x 4 x 4 d = 64 - 32 d = 32 meters Therefore, the car travels a distance of 32 meters during the 4-second interval while being brought to rest uniformly from an initial speed of 16 meters per second.

Explanation:

When a car is brought to rest uniformly, it means that the acceleration is constant throughout the motion. In this case, the acceleration is -4 m/s² as calculated earlier. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity. Using the formula for displacement, we are able to calculate the distance traveled by the car. The term ut represents the distance covered due to the initial velocity, while the term (1/2)at² represents the distance covered due to the acceleration. Substituting the values of initial velocity and acceleration into the formula allows us to find the total distance traveled by the car. In this scenario, the car covers 32 meters during the 4-second interval of uniform deceleration. It is essential to understand the concepts of velocity, acceleration, and displacement to solve such physics problems effectively. By applying the correct formulas and understanding the principles involved, we can calculate distances, speeds, and times accurately in various motion scenarios.
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